Linearly used effects:
monadic and CPS transformations into the linear lambda calculus.

Abstract

We propose a semantic and syntactic framework for modelling
linearly used effects, by giving the monadic transforms
of the computational lambda calculus (considered as the core
calculus of typed call-by-value programming languages) into
the linear lambda calculus. As an instance Berdine et al.'s
work on linearly used continuations can be put in this
general picture. As a technical result we show the full completeness
of the CPS transform into the linear lambda calculus.